Hi all, I am still working on second derivative tests having trouble with finding the critical points.
The problem is find the critical points of f(x,y)=sinx+siny+cos(x+y) for x between 0 and pie/4 and y between 0 and pie/4. Classify each as a local min, max, or saddle point.
I found the partials to be:
derivative of f with respect to x = fx=cosx-sin(x+y)
derivative of f with respect to y = fy=cosy-sin(x+y)
I am having trouble solving the partials for 0.
MIT 18.02 Multivariable Calculus, Fall 2007
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I did this by trial and error. Does anyone know how to solve it algebraically?
First, eliminate sin(x+y):
Plug x=y to either fx or fy:
Very clever!! That makes a lot of sense!! It's amazing how easy it looks once you've seen it done. I have been puzzling over that one for days! Thanks!